Question

Jaxon invested $58,000 in an account paying an interest rate of 2.7% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 14 years?

Answer 1

To calculate the amount of money in the account after 14 years with quarterly compounding interest, you can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.

Given:
- \( P = 58000 \)
- \( r = 0.027 \) (2.7% expressed as a decimal)
- \( n = 4 \) (since the interest is compounded quarterly)
- \( t = 14 \)

Now, substituting the values into the formula:

\[
A = 58000 \left(1 + \frac{0.027}{4}\right)^{4 \times 14}
\]

First, calculate \( \frac{0.027}{4} \):

\[
\frac{0.027}{4} = 0.00675
\]

Now, calculate \( 4 \times 14 = 56 \). So we have:

\[
A = 58000 \left(1 + 0.00675\right)^{56}
\]

Calculating \( 1 + 0.00675 \):

\[
1 + 0.00675 = 1.00675
\]

Now we raise this to the power of 56:

\[
A = 58000 \times (1.00675)^{56}
\]

Calculating \( (1.00675)^{56} \):

\[
(1.00675)^{56} \approx 1.429045
\]

Thus,

\[
A \approx 58000 \times 1.429045 \approx 82844.61
\]

Finally, rounding to the nearest dollar:

\[
A \approx 82845
\]

Therefore, the amount of money in the account after 14 years would be **$82,845**.